Cops never looked into a key piece of evidence in the murder probe of phony doc Dean Faiello, and the flub could foul up the case against the quack, The Post has learned.

Investigators believe Faiello, 44, killed banker Maria Cruz, 35, in a botched cosmetic surgery, then buried her in a concrete tomb at his house in Newark.

But they haven’t figured out how her body got to New Jersey from Faiello’s makeshift office in Chelsea, where he allegedly did the ill-fated procedure April 12, 2003.

They suspect he stuffed the body into a small suitcase and carted it off in his SUV, which was parked at Faiello’s house the day after Cruz died, pals of the fake doc said. But cops failed to search the 1996 Jeep Grand Cherokee or do any forensics tests on it.

“We were aware of the car and determined it was of no investigative value,” said Inspector Michael Coan, a police spokesman.

Police have no witnesses to Cruz’s death and Faiello hasn’t told cops what happened, making the case against him circumstantial.

Two experts agreed that the evidence against Faiello was still strong but said the failure to test the car could hurt the chances of a conviction.

“In my opinion, [the investigators] screwed up,” said Lawrence Kobilinksy, a forensics expert at John Jay College who consults with the NYPD.

“If he transported her, the car is considered one of the crime scenes. A good defense attorney could argue that the police were sloppy.”

Even this late in the game, investigators might find something useful in the Jeep, Callan said.

“Maybe a hair, a fiber, traces of a drug, who knows?”

Faiello, who was hauled back to New York after months on the lam in Costa Rica and pleaded not guilty to second-degree murder Thursday, continued to drive the Jeep in the weeks following Cruz’s death, his pals told The Post.

He sometimes parked it at the home of a neighbor, Mark Ritchey, with whom Faiello lived for five months after Cruz’s disappearance, while Faiello readied his own house to be sold.

Ritchey found Cruz’s purse and ID and told investigators he suspected Faiello stored the suitcase with Cruz’s remains in Ritchey’s garage.

He said he noticed a foul smell there that lasted until May, when cops think Faiello buried the body.

In late August, Faiello was driving the Jeep when he got stopped and arrested on a traffic offense in Belleville, N.J. He had no license, registration or inspection, and the Jeep was impounded by cops.

Three weeks later, he bolted for Costa Rica.

Faiello’s sister, Debra Faiello, a New Jersey state trooper, eventually took title to the car and took the SUV to her house in Milford, N.J. The Post found it sitting in her driveway in February.